Numerical Issues in Space-Geodetic Data Analysis and Their Impact on Earth Orientation Parameters

Space-Geodetic techniques are used to provide fundamental scientific products like the terrestrial and celestial reference frame or the Earth orientation parameters (EOPs). These parameters are typically determined in a least squares adjustment of redundant observations. Within this process, numerical issues materializing in the condition of the equation system as well as in insufficient stability of the solution play an important role. While bad condition numbers are an indicator of numerical problems having no connection to the solution strategy i.e., the algorithms used for solving the equation system, numerical stability refers to the algorithms which are used. This paper focuses on the impact of numerical conditioning on EOPs. Exemplarily for other space-geodetic techniques, we analyze the data analysis of Very Long Baseline Interferometry (VLBI) observations. For VLBI, the equation system of the least squares adjustment is apparently ill-conditioned. Thus, errors of the observations would be amplified during the adjustment process. However, we show that the conditioning is not that bad as it highly depends on the parametrization and we present options to improve the conditioning in VLBI data analysis. We present methods to reveal the relationship between numerical characteristics of the involved matrices and the EOPs.